EXCHANGE 


Standardization  of  Some  of  the 
Common  Tests  Used  in  Deter- 
mining the  Acuteness  of 
Vision  of  School 
Children 


BY 


J.   M.   McCALLIE 

TRENTON,  N.  J. 


A  Thesis  Submitted  to  the  Faculty  of  the 

Graduate  School  of  the  University  of 

Pennsylvania  in  Partial  Fulfilment 

of  the  Requirements  for  the 

Degree  of  Doctor  of 

Philosophy 


STANDARDIZATION  OF  SOME  OF  THE  COMMON 

TESTS    USED    IN    DETERMINING    THE 

ACUTENESS  OF  VISION  OF  SCHOOL 

CHILDREN 


BY 

J.  M.  McCALLIE 

TRENTON,  N.  J. 


A  Thesis  Submitted  to  the  Faculty  of  the  Graduate  School 
of  the  University  of  Pennsylvania  in  Partial  Fulfil- 
ment of  the  Requirements  for  the  Degree  of 
Doctor  of  Philosophy 

June,    1912. 


'   •'         W1H, 

;  : 

1   "w  v.     j.    ^,     K. 


STANDARDIZATION  OF  SOME  ;OF  THE  dO 
TESTS    USED    IN    DETERMINING    THE 
ACUTENESS  OP  VISION  OF  SCHOOL 
CHILDREN 

Most,  if  not  all  of  the  tests,  both  letters  and  characters, 
used  for  testing  the  acuteness  of  school  children  are  based, 
in  theory,  at  least,  upon  the  Snellen  test  letters. 

Since  the  Snellen  letters  will  be  referred  to  often,  a  brief 
account  of  their  origin  and  structure  is  here  given : 

In  1862,  Dr.  Herman  Snellen,  professor  of  ophthalmolgy  in  the  Uni- 
versity of  Utrect,  Holland,  and  director  of  the  Netherlands  Institute  for 
Diseases  of  the  Eyes,  published  an  improved  series  of  test  types  for 
measuring  the  acuity  of  vision.*  The  principle  which  guided  him  in  the 
construction  of  these  test  letters  is  based  upon  the  fact  that  the  normal 
eye  can  just  discern  objects  that  subtend  a  one  minute*  angle,  the  vertex 
of  the  angle  being  the  point  where  the  rays  of  light  cross  before  falling 
on  the  retina. 

In  order  that  a  letter  may  be  recognized  each  one  its  elements  must 
be  discernible^iiejice,  each  of  these  elements  must  have  a  diameter  equal 
to  the  tangent  of  an  angle  oL>at  least  one  mjnute.  In  constructing  uni- 
form letters  in  conformity  with  this  principle,  Snellen  found  that  each 
letter  must  have  at  least  one  diameter  equal  to  the  tangent  of  a  five- 
minute  angle.  Each  letter  is  therefore  made  in  a  square  which  is  sub- 
divided into  twenty-five  equal  squares,  each  small  square  being  equal  in 
diameter  to  the  tangent  of  a  one-minute  angle.  Since  the  tangent  of  a 
five-minute  angle  is  equal  to  0.001454,  to  obtain  the  longest  diameter  of 
a  letter  to  be  seen  at  a  given  distance,  Snellen  multiplied  the  length  of 
the  tangent  of  five  minutes  by  the  distance,  in  centimeters,  of  the  letter 
from  the  nodal  point  of  the  eye;  thus,  at  a  distance  of  one-hundred  cen- 
timeters the  height  of  the  letters  should  be  0.1454  centimeter,  and  each 
stroke  of  the  letter  should  be  at  least  one-fifth  of  this,  or  0.0291  in 
length. 

Before  beginning  the  work  a  large  number  of  test  cards 
were  collected  from  different  dealers.  On  some  of  these 
were  lines  of  letters  of  different  sizes,  on  others,  lines  of 
pictures  or  characters  of  different  sizes.  Under  each  one 
of  these  lines  of  different  sized  letters,  pictures,  or  charac- 
ters, was  printed  the  distance  at  which  they  were  supposed 
to  be  seen  by  the  normal  eye.  An  examination  of  this  col- 


*Snellen,   H.      Optotypi  ad  visum   determinandum   secundum   formu- 

larum  y —    Ed.    XVII.      (Probebuchstaben    zur    Bestimmung    der    Seh- 

scharfe.)      Berlin,  H.   Peters.      1904. 

336267 


lection  of  material  soon  disclosed  the  fact  that  there  was  no 
uniformity  either  in  the  size,  style,  or  structure  of  the  let- 
ters or  characters  or  pictures,  gotten  out  by  different 
houses,  which  were  supposed  to  be  seen  at  the  same  distance 
by  the  normal  eye.  Not  only  was  there  a  lack  of  uniform- 
ity, but,  not  on  a  single  card,  could  there  be  found  a  set  of 
letters  or  characters  or  pictures  whose  proportions  were  in 
accordance  with  the  Snellen  measurements.  And,  not  only 
were  these  out  of  proportion,  according  to  Snellen,  but  they 
were  not  of  the  right  size  to  be  seen  at  the  different  dis- 
tances. The  letters  and  characters  intended  to  be  read  at 
the  shorter  distances  were  generally  printed  so  poorly  as 
to  make  them  useless  as  tests.  Add  to  these  faults  the  facts, 
that  these  letters  and  characters  were  printed  in  black  on 
several-  shades  of  white  or  cream  colored  cardboard  or 
different  shades  of  white  letters  on  black  cards,  and,  that 
the  finish  of  the  cardboard  varied  from  a  glossy  white  or 
black  to  a  lustureless  white  or  black,  and  it  can  readily  be 
seen  that  there  could  be  no  uniformity  of  results,  to  say 
nothing  of  accuracy  or  the  possibility  of  selecting  any  one 
of  these  measures  for  a  standard.  It  was  evident,  there- 
fore, that  if  my  work  was  to  have  any  value,  new  letters 
must  be  made.  This  was  done  by  most  accurately  drawing 
the  letters  according  to  the  Snellen  dimensions  from  which 
new  and  accurate  type  were  made,  and,  from  which,  the 
letters  used  in  these  tests  were  printed,  except  the  tests 
made  in  comparing  the  relative  visibility  of  the  "illiterate 
E,"  with  the  16  ft.  letters. 

The  picture  tests  were  discarded  because  they  were  not 
and  could  not  be  constructed  according  to  the  Snellen 
measurements,  consequently  the  results  obtained  could  not 
be  compared  with  results  obtained  by  tests  made  with  the 
Snellen  letters. 

The  tests  made  were  divided  into  two  parts.  The  first 
had  to  do  with  the  visibility  of  the  "illiterate  E,"  supposed 
to  be  seen  by  the  normal  eye  at  no  greater  distance  than 
16  ft.,  as  compared  with  the  visibility  of  the  Snellen  letters 
constructed  to  be  seen  by  the  normal  eye  at  no  greater  dis- 
tance than  16  ft. 

The  second  part  had  to  do  with  determining  whether 
tests  made  by  the  Snellen  12  ft.,  or  16  ft.  letters,  or  a  dot, 


supposed  to  be  seen  at  20  ft.,  are  not  as  accurate  as  tests 
made  with  letters  to  be  seen  50  ft.,  40  ft.,  30  ft.,  or  20  ft. 

The  following  is  a  detailed  description  of  the  method 
and  results  obtained  by  comparing  the  visibility  of  the 
"illiterate  E"  with  the  Snellen  test  letters  of  the  same  di- 
mensions : 

As  stated  above,  types  for  the  16  ft.  "illiterate  E"  and 
the  16  ft.  letters  were  not  made  anew.  This  was  not  neces- 
sary because  a  copy  of  Snellen 's  classic  work  on  test  types 
was  found  which  contained  the  "illiterate  E"  and  the  let- 
ters of  the  desired  size.  The  letters  taken  from  this  book 
were  O,  L,  N,  Z,  B,  D,  T,  and  E,  and  the  "illiterate  E" 
turned  up,  down,  right,  and  left,  (see  Fig.  1)  all  of  which 
were  supposed  to  be  visible  to  the  normal  eye  at  16  ft. 
These  were  printed  on  white  unglazed  paper  about  the 
thickness  of  ordinary  book  paper. 

The  16  ft.  letters  and  the  16  ft.  "illiterate  E,"  were 
selected  of  one  and  the  same  size  to  enable  comparison  af 
results  to  be  made  more  readily  and  because  the  size  of  the 
rooms  in  which  the  tests  were  made  would  not  admit  of 
using  larger  letters. 

Each  one  of  these  letters  and  "illiterate  E's,"  were 
carefully  cut  out,  and  pasted  on  white  unglazed  cards, 
three  and  one-half  by  six  inches,  one  and  one-half  inch 
from  the  top  of  the  card  and  equally  distant  from  the  sides, 
one  letter  or  one  "  illiterate  E"  on  a  single  card.  On  the 
back  of  each  card  was  written  the  same  letter  or  '  *  illiterate 
E"  that  appeared  on  the  front.  This  was  for  the  purpose 
of  enabling  the  operator  to  know  the  letter  or  to  tell  which 
way  the  "illiterate  E,"  was  turned,  when  presented  to  the 
subject. 

By  having  the  letters  on  separate  cards,  so  that  only 
one  letter  was  in  view  at  a  time,  the  operator  could  be 
sure  that  the  pupil's  reply  was  a  judgment  on  that  letter 
and  not  on  some  other  letter,  as  often  happens  when  several 
letters  are  shown  at  one  time.  This  arrangement,  also, 
made  it  possible  to  vary  the  order  of  presentation,  and,  so 
prevent  the  letters  from  being  memorized.  The  operator 
by  this  device  was  left  free  to  give  his  entire  attention  to 
the  efforts  put  forth  by  the  children  in  reading  the  letters. 
By  holding  the  cards  in  his  hands,  the  operator  was  enabled 


to  utilize  the  best  light  in  the  room  more  easily  than  if  he 
had  used  a  large  card  hung  on  the  wall,  as  is  usually  done 
in  such  tests. 

The  best  position  for  exhibiting  the  letters,  so  far  as 
light  was  concerned,  was  selected,  and,  beginning  with  this 
position,  short  chalk  marks  were  made  on  the  floor  every 
two  feet  the  entire  length  of  the  room,  the  first  mark  being- 
two  feet  away  from  the  position  selected  for  best  light,  the 
second  four,  and  so  on. 

Everything  being  ready,  the  pupils  were  called  one  at  a 
time  and  told  to  stand  with  their  toes  to  line  twenty,  with  a 
card  held  over  one  eye.  Two  or  three  letters  were  pre- 
sented. If  the  pupil  could  not  read  them,  he  was  asked  to 
step  up  two  feet  and  try  again.  If  he  failed  again,  he  was 
asked  to  step  up  two  more  feet  and  try  again.  If  he  failed 
at  this  distance — sixteen  feet — he  was  asked  to  step  up 
one  foot  at  a  time,  after  each  succeeding  failure,  until  he 
was  able  to  read  at  least  five  consecutive  letters  correctly. 
The  letters  were  not  exposed  to  view  longer  than  two  sec- 
onds. If  the  correct  names  of  five  consecutive  letters  could 
not  be  read  in  the  time  limit,  the  result  was  counted  a  fail- 
ure, until  a  distance  was  found  where  the  letters  could  be 
read.  If  the  subject  could  read  all  the  letters  correctly  at 
sixteen  feet,  this  fact  was  indicated  by  placing  the  fraction 
16/16  opposite  his  name  on  the  record  sheet.  If  he  could 
read  the  letters  only  at  six  feet,  this  fact  was  indicated  by 
the  fraction  6/16.  If  the  letters  could  be  read  at  twenty- 
four  feet,  this  fact  was  represented  by  the  fraction  24/16, 
etc. 

Having  determined  the  greatest  distance  at  which  one 
eye  could  read  the  letters,  the  same  process  was  repeated 
with  the  other  eye.  Immediately  after  each  pupil  was  test- 
ed with  the  alphabet  cards  he  was  tested  with  the  * '  illiterate 
E,"  cards,  by  the  same  general  method,  except  that  instead 
of  naming  the  character  the  pupil  was  required  to  point  in 
the  direction,  up,  down,  right,  or  left,  thus  indicating  the 
direction  of  the  opening  of  the  E.  In  this  case,  as  with  the 
letters,  a  single  error  was  taken  to  indicate  that  the  pupil's 
vision  was  not  sufficiently  acute  to  read  the  characters  at 
that  particular  distance,  and  he  was  required  to  move  to- 
ward the  cards  until  he  reached  the  point  at  which  at  least 


five  consecutive  characters  could  be  read  correctly  within 
the  allotted  time  of  not  more  than  two  seconds  each. 

In  doing  this  work  the  tests  with  the  "illiterate  E,"  al- 
ways followed  the  test  with  the  letters,  so,  if  fatigue  played 
any  part  in  the  tests  it  would  show  itself  in  the  results  ob- 
tained with  the  "illiterate  E." 

Before  beginning  the  test  each  day,  the  operator  tested 
his  own  vision  to  see  whether  the  light  was  satisfactory. 
Tests  were  made  only  on  days  when  the  light  was  good.  No 
work  was  done  on  cloudy  or  dark  days.  These  tests  were 
carried  on  in  the  different  class-rooms,  and>  so  far  as  each 
pupil  was  concerned  the  test  with  the  "illiterate  E,"  and 
the  letters  were  made  under  exactly  the  same  conditions. 

470  children  took  the  tests  during  the  months  of  April 
and  May. 

The  results  of  these  tests  are  presented  in  the  table  I. 
This  shows  the  number  of  eyes  tested  in  grades  I  to  VIII, 
with  the  greatest  distances  at  which  the  alphabet  and  illit- 
erate characters  could  be  distinguished,  Four  hundred  and 
seventy  pupils,  or  940  eyes,  were  tested.  These  pupils  were 
distributed  throughout  the  grades  as  follows:  72  in  the 
first  grade,  54  in  the  second,  39  in  the  third,  28  in  the  fourth, 
41  in  the  fifth,  29  in  the  sixth,  130  in  the  seventh  and  77  in 
the  eighth.  The  344  pupils  in  grades  III  to  VIII,  inclusive, 
were  tested  with  both  the  alphabet  and  illiterate  characters. 
In  columns  headed  Totals  II  to  VIII,  may  be  found  the  fig- 
ures affording  the  most  ready  comparison  of  the  results 
with  the  alphabet  characters,  and  illiterate  cards.  Thus, 
with  the  alphabet  characters,  the  largest  number  of  eyes, 
148,  distinguished  the  letters  at  fourteen  feet;  the  next 
largest  128,  at  sixteen  feet,  and  the  next  largest  114,  at 
twelve  feet.  Of  these  688  eyes  tested,  390,  or  56.7  per  cent., 
distinguished  the  letters  at  from  twelve  to  sixteen  feet. 
With  the  illiterate  cards,  however,  these  same  eyes  dis- 
tinguished the  "illiterate  E"  at  a  much  greater  distance, 
in  fact,  94  pupils  saw  the  "illiterate  E,"  at  twenty- two  feet. 
This  was  the  largest  number  seeing  this  character  at  any 
distance,  and  the  next  largest  number,  92,  saw  it  at  twenty- 
four  feet.  The  next  largest  number,  86,  saw  it  at  twenty 
feet.  The  results  of  this  comparative  test  with  two 
characters  are  graphically  exhibited  in  Graph  I.  Curve  I 


^t&.ji.cococococoiototototoi-'i-'Mi-'i-' 
i—1  co  >^  to 

I— i    tO    tO   tO    M 
OOOOO5CO4^.MO5OOOOenen-qcotOCO!— 'O5enOI— 'I— 'OO 

i— '  to  *>.  en  ,£.  co  to 

lOtOCO4^4^tOl— 'tOI— ' 

I— '  (— ' 

OOOOOOOOOOOCnCOOOCTtOOStOh-'tOOOOOOh-' 

to  to  i— ' 
oooooooooooocooscototo-joeni-'i-'i-ii-'o 

tO    h- ' 

ooooi-'enosoooen^ooi-'^coo^i-'MOi-'OOOo 

OOOOOOOOOOOOt005OO-<II-'iXit-iOOOOO 

I—1    tO 
OOOOOOOOOOOOOO5I— '-J-JCO 

—  I— ' 


Q 


H 

CD 


CO 


^ 

&   O 


9 


CURVE   I. 


' 


CURVE   II. 


CL  3 

CO     p 


% 


to  4^.  en  to  i—1  to  M 

t—  ltOO5h-iaih-'OO?C>O 

CURVE   III. 


tocotnooOt^.i-'Ooo^cotototo 

Ol-'05^.OOOtnl-'l-iCn«D^Ot0 

CURVE   IV. 


9 


represents  the  results  of  the  alphabet  test  and  Curve  II 
represents  the  results  of  the  "  illiterate.  E"  test. 

The  pupils  of  the  first  and  second  grades,  126  in  all, 
were  tested  with  the  "illiterate  E"  only,  because  they  did 
not  all  know  the  letters  of  the  alphabet.  Curve  III  repre- 
sents the  results  obtained  by  testing  these  252  eyes  with  the 
illiterate  cards.  Curve  IV  combines  in  a  single  curve  the 
results  of  the  illiterate  test  with  the  470  pupils  in  all  grades. 


Z468l0tZt416  M&XZ4&&XX  34  36  38  40  4Z4* 
GKAPH  1. 

The  straight  line  a-b,  running  perpendicularly  through 
the  curves,  is  the  line  of  assumed  normal  vision  for  all  of 
the  tests.  If  this  were  correct,  then  all  of  the  eyes  repre- 
sented by  the  portion  of  the  curves  to  the  left  of  this  line 
are  subnormal,  and  all  eyes  represented  by  that  portion  of 
the  curve  to  the  right  of  the  perpendicular  are  above  nor- 
mal in  acuteness. 

From  these  curves  we  deduce  the  following  results : 


Curve  I    (alphabet  test)  .  . 
Curve  III    ("illiterate   E") 


Eyes  Normal 

128    or   18.6% 

27   or      3.9% 


Eyes  Subnormal 

453    or   65.8% 

56   or      8.1% 


10 

Eyes  Above  Normal 

Curve    I    (alphabet   test) 107   or  15.5% 

Curve   III    ("illiterate   E") 566   or   82.2% 

It  is  evident  at  a  glance,  that  something  is  wrong,  either 
with  the  letters  used  or  with  the  "illiterate  E,"  since  the 
results  were  obtained  under  exactly  the  same  conditions. 
It  is  not  possible  for  both  results  to  be  correct,  because  with 
the  "illiterate  E,"  8.1  per  cent,  of  the  pupils  tested  were 
subnormal  and  82.2  per  cent,  were  above  normal ;  whereas, 
with  the  alphabet  test,  65.8  per  cent,  of  the  same  pupils 
were  found  to  be  subnormal  and  only  15.5  per  cent,  above 
normal.  The  fact  that  only  3.9  per  cent,  of  the  pupils,  ac- 
cording to  the  illiterate  test,  had  normal  vision,  and  only 
8.1  per  cent,  were  subnormal,  would  warrant  the  suspicion 
that  something  was  wrong  with  the  "illiterate  E,"  as  a 
reliable  measure  for  acuteness  of  vision.  A  close  analysis 
of  this  character  will  prove  that  the  suspicion  is  well  found- 
ed. The  structure  of  the  "E"  is  shown  at  the  right  of 
Graph  I. 

A  pupil  being  tested  with  this  character  has  only  to  de- 
termine in  which  one  of  the  four  directions  up,  down,  right, 
or.  left,  the  opening  of  the  character  is  directed,  and  this 
opening  can  always  be  pointed  out  by  observing  that  this 
side  of  the  E  is  always  the  lightest.  Each  of  these  char- 
acters, as  before  stated,  is  constructed  in  a  square  which  is 
subdivided  into  twenty-five  squares.  The  normal  eye  is 
supposed  to  be  able  to  discern  one  of  these  small  squares 
at  the  same  distance  at  which  the  E,  turned  in  different 
directions  can  be  recognized.  It  will  be  observed  that  there 
are  three  of  these  small  squares  lying  together  unfilled  on 
the  open  side  of  this  character.  Four  of  these  small 
squares,  arranged  in  the  form  of  a  square  has  twice  the 
diameter  of  the  small  square  and  should  be  discerned  at 
twice  the  distance  or  32  feet.  It  would,  therefore,  be  rea- 
sonable to  suppose  that  these  three  unfilled  squares  lying 
one  above  the  other  should  be  seen  at  about  three-quarters 
of  that  distance,  or  twenty-four  feet.  As  a  matter  of  fact, 
this  is  exactly  the  distance  at  which  they  were  discerned  by 
the  largest  number  of  the  pupils  of  all  grades. 

This  comparative  test  proves  conclusively  that  sixteen 
feet  is  not  the  distance  at  which  the  normal  eye  can  just 


11 

discern  the  "illiterate  E."  In  fact,  twenty-nine  eyes  were 
found,  exhibiting  normal  vision  with  the  alphabet  test, 
that  could  interpret  these  characters  at  twice  sixteen  feet. 
Many  could  read  them  farther  than  thirty-two  feet,  in  fact, 
two  could  do  this  at  forty-four  feet  and  one  could  make 
them  out  at  fifty  feet. 

It  is  evident  then,  that  if  this  character  is  to  be  used 
for  testing  the  acuteness  of  vision,  a  new  distance,  at  which 
the  normal  eye  can  just  see  it,  must  be  determined  or  the 
size  of  the  characters  must  be  changed.  Either  or  both  of 
these  changes  can  easily  be  deduced  from  the  results  ob- 
tained by  these  tests. 

Assuming  that  sixteen  feet  is  the  distance  at  which  the 
sixteen  foot  letter  can  just  be  made  out,  by  the  average 
normal  eye,  then,  the  same  relative  variation  from  this 
normal  sixteen  foot  distance,  would  be  found  to  obtain  in 
any  sized  letter  or  characters  used  in  a  series  of  tests.  For 
example,  if  a  series  of  tests  with  the  sixteen  foot  letter, 
should  show  that  the  eyes  tested  could  see  the  letters  at  an 
average  distance  of  only  twelve  feet,  or  one-fourth  less  than 
normal  distance,  and,  if  another  series  of  tests,  made  on 
the  same  eyes  with  another  set  of  letters  of  any  given  uni- 
form size  and  structure,  should  show  that  they  could  be 
seen  at  twenty-four  feet,  then  the  distance,  twenty-four 
feet,  should  vary  as  much  from  the  normal  distance,  at 
which  such  letters  should  be  seen,  as  twelve  feet  varies  from 
sixteen  feet,  the  normal  distance  at  which  the  sixteen  foot 
letters  should  be  seen.  It  is  evident  that  the  distance 
twelve  feet  is  one-fourth  less  than  the  normal  distance  six- 
teen feet,  and,  since  the  same  relation  must  exist  in  the 
series  of  tests  which  showed  that  the  average  distance  at 
which  letters  or  characters  could  be  seen  was  twenty-four 
feet,  then  this  distance,  twenty-four  feet  is  one  fourth  less 
than,  or  three-fourths  of  the  distance  at  which  the  normal 
eye  can  see  these  letters  or  characters.  If  twenty-four  feet 
is  three-fourths  of  this  normal  distance,  then  the  distance 
at  which  the  normal  eye  should  see  these  letters  or  char- 
acters is,  4/3  of  24  ft.,  or  32  ft. 

In  the  series  of  tests  described  above  it  was  found  that 
the  average  distance  at  which  the  688  eyes  could  just  see  the 
sixteen  foot  letters  was  13.7  ft.,  and  the  average  distance 
at  which  the  same  688  eyes  could  see  the  "illiterate  E,"  at 


12 

the  same  time  was  23.2  ft.  The  distance  at  which  the  nor- 
mal eye  can  see  the  sixteen  foot  letters  is  16/13.7  of 
the  average  distance  at  which  the  letters  were  seen.  Since 
the  same  relations  must  exist  between  the  normal  distance 
at  which  the  "  illiterate  E,"  can  be  seen  and  the  average 
distance  at  which  it  was  seen,  we  find  this  normal  distance 
by  taking  16/13.7  of  23.2/1  ft.,  the  distance  at  which  the 
"illiterate  E"  could  be  seen.  This  gives  26.4  ft.,  which  is 
the  distance  at  which  the  normal  eye  can  see  the  ' '  illiterate 
E"  used  in  these  tests,  instead  of  sixteen  feet  as  was  given 
by  Snellen. 

If  it  is  desired  to  change  the  size  of  the  "illiterate  E," 
so  that  it  can  just  be  read  at  sixteen  feet,  instead  of  chang- 
ing the  distance  at  which  it  can  just  be  seen,  this  can  be 
readily  done  by  making  it  just  16/26.4  of  the  size  used  in 
these  tests.  As  these  tests  clearly  show,  one  or  the  other 
of  these  changes  should  be  made  if  the  "illiterate  E"  is  to 
be  used  as  a  test. 

The  second  part  of  the  problem  has  as  its  object,  as 
already  stated,  the  determination  of  whether  the  Snellen 
12  ft.,  or  a  16  ft.  letter,  or  a  black  dot  whose  diameter  is 
one-fifth  the  greatest  diameter  of  a  Snellen  20  ft.  letter, 
might  not  be  as  reliable  tests  for  acuteness  of  vision  as  the 
tests  made  with  the  Snellen  20  ft.,  30  ft.,  40  ft.,  or  50  ft. 
letters. 

The  vision  of  200  pupils  in  the  fifth,  sixth,  seventh,  and 
eighth  grades  of  a  public  school  were  tested  in  arriving  at 
a  solution  of  the  second  part  of  the  problem. 

The  following  is  a  description  of  the  method  used  in 
making  these  comparative  tests: 

The  tests  were  made  in  a  room  about  90  ft.  long,  near 
one  end  of  which  was  a  window  so  situated  as  to  give  an 
excellent  light,  in  which  to  exhibit  the  letters  in  making  the 
tests.  A  chalk  mark  was  placed  on  the  floor  at  the  point 
where  the  light  was  best.  Measuring  from  this  line,  a  chalk 
mark  was  placed  on  the  floor  every  two  feet  for  the  entire 
remaining  length  of  the  room  which  was  84  ft.  These  marks 
were  numbered  as  follows :  the  first  line,  made  on  the  floor 
at  the  point  of  best  light,  was  marked  0 ;  the  next  line,  two 
feet  away,  2 ;  the  next  line,  4 ;  the  next,  6,  etc.,  up  to  84.  This 
gave  a  clear  range  of  vision  of  84  feet. 


13 

It  was  decided  beforehand  that  the  letters  and  dots 
should  be  exhibited  one  at  a  time  and  that  each  should  be 
exposed  to  view  not  longer  than  two  seconds. 

As  stated  above,  it  was  not  possible  to  find  test  cards 
printed  in  clear  type  of  the  right  dimensions,  and,  it  was 
also  impossible  to  use  these  test  cards  for  testing  pupils 
with  the  different  sized  letters  without  some  of  the  letters 
being  memorized,  thus  thwarting  the  purpose  of  the  tests. 
To  overcome  these  difficulties,  it  was  found  not  only  neces- 
sary to  have  new  types  constructed  with  the  correct  dimen- 
sions, according  to  the  Snellen  measurements,  but  to  de- 
vise entirely  new  vision  test  cards.  These  cards  serve  the 
double  purpose  of  allowing  only  one  letter  to  be  seen  at  a 
time,  and  rendering  it  impossible  for  anyone  to  remember 
the  order  of  the  letters,  and,  beside,  the  tests  can  be  made 
with  much  greater  ease,  accuracy,  and  rapidity  than  can  be 
done  with  the  ordinary  test  cards. 

A  set  of  these  new  test  cards  consists  of  twelve  square 
cards  about  5  in.  x  5  in.,  on  which  are  printed  forty-eight 
letters  of  four  sizes,  one  letter  of  each  size  on  each  card,  no 
two  cards  having  the  same  letters  on  them.  The  different 
sized  letters  can  be  seen  by  the  normal  eye  at  20  ft.,  30  ft., 
40  ft.,  and  50  ft.,  respectively.  These  four  letters,  on  each 
card,  are  placed  so  that  one  appears  one-half  inch  from  each 
margin  and  equally  distant  from  the  sides.  And  they  are 
printed  in  such  a  way  that  only  the  letter  at  the  top  of  the 
card  is  in  a  position  to  be  read  when  the  card  is  held  in  an 
upright  position. 

A  reduced  copy  of  one  of  these  cards  is  shown  in  Fig.  2. 

The  tests  are  made  with  these'  cards  exactly  as  tests 
are  made  with  the  ordinary  test  cards,  except  that  the  oper- 
ator holds  the  cards  in  his  hand  and  exhibits  one  letter  at 
a  time,  by  taking  the  cards  one  at  a  time,  from  the  back  of 
the  pack  and  placing  them  in  front.  Any  one  of  the  four 
sized  letters  may  be  used  by  simply  giving  the  cards  a 
quarter  or  a  half  turn  in  the  hands.  Any  possibility  of  re- 
membering the  order  of  the  letters  may  be  prevented  by 
now  and  then  shuffling  the  cards.  This  makes  it  possible  to 
test  pupils  in  their  own  rooms  and  in  the  presence  of  all 
the  pupils  if  desired,  and  obtain  trustworthy  results. 

In  making  tests  with  the  black  dots  which  were  sup- 
posed to  be  seen  at  20  ft.,  the  first  thing  to  consider  was  the 


14 


T 


0 


Figure  2.  Showing  the  four  sizes  of  letters  and  their 
arrangement  on  one  of  the  twelve  cards  used  in  these  tests.- 
The  smallest  of  these  letters  can  be  seen  by  the  normal  eye 
at  20  ft. ;  the  next  larger,  30  ft. ;  the  next  larger,  40  ft. ;  and 
the  largest,  50  ft. 


15 

size  of  the  dot.  According  to  the  rule  laid  down  by  Snellen, 
the  normal  eye  can  just  discern  an  object  whose  largest  di- 
ameter is  one-fifth  of  that  of  a  letter  which  can  just  be  dis- 
cerned at  the  same  distance.  A  letter  to  be  just  discerned 
at  20  ft.  should  be  0.349  inches  in  height  or  in  the  largest 
diameter,  so,  the  size  of  the  dot  to  be  seen  at  20  ft.,  should 
be  one-fifth  of  0.349  inches  or  0.0695  inches  in  diameter. 
Accordingly,  a  dot  as  nearly  this  dimension  as  possible  was 
carefully  constructed. 

To  e'nable  one  to  make  tests  with  the  dot  rapidly  and  to 
add  interest  to  the  work,  another  set  of  test  cards  was  de- 
vised embodying  the  following,  somewhat  novel  features, 
as  shown  in  Fig.  3,  Fig.  4,  Fig.  5,  and  Fig.  6. 

It  takes  ten  of  these  cards  to  make  a  set.  The  dot  in  the 
ring  is  the  object  to  be  seen.  There  are  three  cards  with 
the  dot  in  the  boy's  ring;  three  with  the  dot  in  the  girl's 
ring ;  three  with  the  dot  in  the  bear 's  ring ;  and  one  with  no 
dot  in  either  ring.  All  of  the  dots  are  identical  in  size. 

The  boy,  girl,  and  bear  are  supposed  to  be  playing  ball, 
and  each  player  is  supposed  to  be  trying  to  catch  the  ball 
in  his  racket.  The  dot  is  the  ball  and  the  rings  are  rackets. 

The  tests  were  made  in  this  way :  The  pupil  to  be  tested 
was  placed-  at  the  distance  where  the  normal  eye  can  just 
see  the  dot.  The  operator  shuffled  the  cards  and  then  held 
them  up  face  toward  the  pupil.  As  the  cards  were  taken 
from  the  back  of  the  pack  and  placed  in  front,  the  pupil 
was  required  to  tell  which  had  the  ball,  by  saying  "boy," 
"bear,"  etc.,  or,  if  he  did  not  see  the  dot  at  all,  by  saying 
"nobody  has  it."  This  method,  wras  found  to  have  the 
great  advantage  of  being  easily  understood  by  children  and 
interesting  to  them.  Even  pupils  in  the  kindergarten  may 
be  tested  with  these  cards  used  as  a  game. 

Having  determined  the  kind  of  tests  to  be  used  and 
selected  the  position  for  the  best  light  in  which  to  exhibit 
the  tests,  and  having  marked  off  the  floor  as  in  making  the 
tests  with  the  "illiterate  E"  and  the  16  ft.  letters,  and  hav- 
ing swung  a  pendulum  to  beat  seconds,  the  testing  pro- 
ceeded as  follows : 

An  assistant  took  a  set  of  the  alphabet  test  cards  and 
holding  them  in  front  of  him  in  his  two  hands,  took  a  card 
from  the  back  and  put  it  in  front  every  two  seconds,  accord- 


16 


Figure  3.     Dot  test  for  acuteness  of  vision  showing  one 
position  of  the  dot. 


17 


Figure  4.     Dot  test  for   acuteness   of  vision   showing- 
absence  of  dot. 


18 


Figure  5.     Dot  test  for  acuteness   of  vision  showing 
a  second  position  of  the  dot. 


19 


Figure  6.     Dot  test  for  acuteness  of  vision  showing  a 
third  position  of  the  dot. 


20 

ing  to  the  beat  of  the  pendulum.  The  cards  were  required  to 
be  held  in  the  proper  position  to  receive  the  best  light. 

The  operator  then,  instructing  the  assistant  to  show 
the  fifty  foot  letters,  placed  the  subject  with  his  toes  to 
some  mark  beyond  the  fifty  foot  mark,  say  60  ft.,  and  re- 
quired him,  with  both  eyes  open,  to  name  the  letters  as  they 
were  presented  by  the  assistant.  If  he  could  not  correctly 
name  five  letters  consecutively,  he  was  instructed  to  move 
up  two  feet  and  try  again.  If  he  still  failed  to  name  cor- 
rectly, the  five  letters  consecutively,  he  was  required  to 
move  up  two  feet  more  and  try  again,  and  so  on,  until  a 
position  was  found  where  he  could  read  the  required  num- 
ber of  letters  consecutively.  If  it  was  found  that  the  sub- 
ject could  read  with  ease  all  the  letters  while  on  the  60  ft. 
line,  then  he  was  required  to  move  back  two  or  more  feet  at 
a  time  until  a  position  was  found,  where,  at  least  five  con- 
secutive letters  could  just  be  read.  When  it  was  evident 
to  the  operator  that  mistakes  were  due  to  inattention  or 
other  causes  than  inability  to  see,  another  trial  was  allowed. 

After  the  distance  at  which  the  50  ft.  letters  could  just 
be  seen  was  found,  the  distances  at  which  the  30  ft.  and  20 
ft.  letters  could  just  be  seen  was  determined  in  the  same 
manner. 

The  determination,  at  which  the  20  ft.  dot  could  just  be 
seen  followed  the  test  with  the  20  ft.  letters,  and  was  car- 
ried out  in  this  way:  The  operator  held  in  his  hands  the 
set  of  ten  cards,  described  above,  and  presented  them  in  the 
same  manner  as  in  making  tests  with  the  cards  containing 
the  alphabet.  However,  as  none  of  the  pupils  understood 
what  they  were  to  do  in  this  test,  the  method  was  explained 
to  each  pupil  or  several  at  a  time  by  showing  them  the  cards 
by  saying,  "  Pupils  the  boy,  girl,  and  bear  are  playing  a 
game  of  ball.  The  dot  is  the  ball.  As  each  new  card  is  pre- 
sented the  dot  changes  position  from  the  ring  or  racket  of 
any  one  of  the  players  to  either  of  the  other  two  players,  or 
the  one  having  the  ball  may  keep  it  through  one  or  more 
changes.  As  in  a  real  game,  the  ball  may  be  lost,  so,  in 
this  game,  and  the  lost  ball  is  indicated  by  a  card  being  pre- 
sented on  which  no  ring  contains  a  dot.  Now,  you  are  to 
be  the  umpire  of  the  game  and  your  duty  will  be  to  tell  who 
has  the  ball  as  the  cards  are  changed. "  A  few  cards  were 
then  presented  and  the  pupils  were  required  to  tell  who  had 


21 

the  ball.  When  the  game  was  understood,  the  pupil  to  be 
tested  was  told  to  stand  at  the  16  ft.  or  18  ft.  line  and  try 
seeing  the  dot  a  few  times.  After  he  saw  it  at  this  distance 
he  was  required  to  move  back  two  or  more  feet  at  a  time 
and  try  again,  and  so  on,  until  a  distance  was  found,  at 
which,  the  dots  or  blanks  on  five  consecutive  cards  could 
just  be  made  out.  This  distance  was  recorded  as  the  dis- 
tance at  which  the  dot  could  just  be  seen. 

When  through  testing  with  the  20  ft.  dot,  the  subject 
was  then  tested  with  the  16  ft.  letter  and  then  with  the  12  ft. 
letter,  exactly  in  the  same  manner  as  the  tests  were  made 
with  the  50  ft.,  40  ft.,  30  ft.,  and  20  ft.,  letters.  In  passing 
pupils  through  each  of  these  seven  tests  consecutively,  it 
was  found  that  results  were  often  modified  by  the  eyes  be- 
coming fatigued.  When  this  was  found  to  be  the  case,  the 
subject  was  allowed  to  rest  for  a  short  while. 

Realizing  that  fatigue  might  modify  results  if  each  one 
of  the  200  pupils  were  tested  first  with  the  50  ft.  letter,  then 
the  40  ft.  and  so  on,  down  to  the  12  ft.  letter,  every  other 
pupil  began  his  test  with  the  12  ft.  letter,  then  took  the  16 
ft.  letter,  then  the  20  ft.  letter  and  so  on,  up  to  the  50  ft. 
letter.  By  this  method  it  can  readily  be  seen  that,  what- 
ever effects  fatigue  might  produce,  this  effect  would  be 
equally  distributed,  and  consequently,  it  would  be  non- 
effective,  so  far  as  the  purpose  of  these  tests  is  concerned. 

These  tests  were  conducted  for  each  pupil  in  the  same 
room,  and  with  the  same  kind  of  daylight  as  far  as  possi- 
ble. Care  was  taken  not  to  make  tests  on  cloudy  or  dark 
days. 

Since  the  purpose  of  these  tests  was  to  find  out  how  far 
each  pupil  could  see  the  different  sized  letters  and  the  dot, 
or  how  acute  vision  was,  the  pupils  were  allowed  to  use 
both  eyes  at  once.  This  was  done  because  looking  with  the 
two  eyes  is  the  normal  way  of  seeing  things,  consequently, 
it  is  believed  that  the  results  obtained  more  nearly  repre- 
sent the  true  acuteness  of  vision  of  the  pupils  tested,  than 
if  each  eye  had  been  tested  separately.  Pupils  wearing 
glasses  were  tested  with  their  glasses  on. 

Tables  2,  3,  4,  5,  6,  7  and  8,  pages  23-27,  show  in  detail 
one  phase  of  the  results  of  these  tests. 


22 

Column  (A)  gives  the  number  of  pupils  who  saw  the  dot 
or  letters  at  the  same  greatest  distance. 

Column  (B)  hsows  the  greatest  distances  at  which  the 
different  groups  of  pupils  in  column  (A)  could  see  the  dot 
or  letter. 

Column  (C)  gives  the  combined  distances  at  which  the 
groups  of  pupils  in  (A)  could  see  the  dot  or  different  sized 
letters. 

In  each  of  these  tables  the  sum  of  column  (A)  equals 
200,  the  total  number  of  pupils  tested.  The  sum  of  column 
(C)  in  each  table  equals  the  total  combined  distance  at 
which  all  of  the  200  pupils  could  see  the  letters  or  dot 
used  in  the  test.  Therefore,  it  is  evident  that  if  these  total 
combined  distances  in  each  table  were  divided  by  200,  the 
number  of  pupils  tested,  the  result  will  be  the  average 
greatest  distance  at  which  these  pupils  could  see  the  letters 
or  dots  with  which  they  were  being  tested.  The  perform- 
ance of  this  operation  gives  the  following  results : 

The  total  combined  distance  at  which  the  200  pupils  saw 
the  50  ft.  letters  is  10,894  ft.  This  divided  by  200  gives 
54.47  ft.  as  the  average  distance  at  which  the  50  ft.  letters 
were  seen. 


23 


TABLE  2. 
Results  obtained  by  the  tests  made  with  the  50  ft.  letter : 


(A) 
3 
1 
1 
4 
1 
3 
6 

19 

7 

13 
10 
10 
16 

56 

15 
13 
18 
14 
17 

77 

12 
1 
7 
3 
1 


(B) 

82 
80 
78 
76 
74 
72 
70 


68 
66 
64 
62 
60 


58 
56 
54 
52 
50 


48 
46 
44 
42 
40 


(C) 

246 

80 

78 

304 

74 

216 

420 

1418 

476 
858 
640 
620 
960 

3554 

870 
728 
972 
728 
850 

4148 

576 
.  46 
308 
126 
40 


(A) 
3 
2 
6 
3 
0 

14 


(B) 

38 
36 
34 
32 
30 


(C) 
114 

72 

204 

96 

00 

486 


1 

28 

28 

0 

26 

00 

3 

24 

72 

1 

22 

22 

1 

20 

20 

142 


1 

18 

18 

0 

16 

00 

1 

14 

14 

0 

12 

00 

1 

10 

10 

1 

8 

8 

4 

50 

200 

10894ft. 

Average  distance:  54.5  ft. 


24 


1096 


24 


TABLE  3. 
Results  obtained  by  tests  made  with  the  40  ft.  letters : 


(A) 


21 
14 
19 
20 
30 


(B) 


48 
46 
44 
42 
40 


(C) 


1008 
644 
836 
840 

1200 


(A) 


200 


(B) 


(C) 


1 

74 

74 

5 

28 

140 

1 

72 

72 

3 

26 

78 

0 

70 

00 

2 

24 

48 

0 

68 

00 

2 

22 

44 

0 

66 

00 

0 

20 

00 

0 

64 

00 

— 

— 



5 

62 

310 

12 

310 

3 

60 

180 

— 

— 

•  

o 

18 

00 

10 

636 

2 

16 

32 

o 

14 

00 

3 

58 

174 

1 

12 

12 

8 

56 

448 

1 

10 

10 

8 

54 

432 

1 

8 

8 

9 

52 

468 

0 

6 

0 

11 

50 

550 

0 

4 

0 

1 

3 

3 

on 

O  AT  O 

65 


8625  ft. 


Average  distance:  43.13  ft. 


104 


4528 


10 

5 
4 
4 


38 
36 
34 
32 
30 


380 

180 
136 
128 
180 


1004 


25 


TABLE  4. 


Results  obtained  by  tests  made  with  the  30  ft.  letters : 


(A) 

(B) 

(C) 

(A) 

(B) 

(C) 

1 

60 

60 

2 

18 

36 

1 

58 

58 

1 

16 

16 

1 

56 

56 

2 

14 

28 

0 

54 

00 

0 

12 

00 

0 

52 

00 

2 

10 

20 

0 

50 

00 

0 

8 

00 





.  

2 

6 

12 

3 

174 

0 

4 

00 

1 

3 

3 

4 

.   48 

192 

5 

46 

A  A 

230 

o  c  o 

10 

115 

8 
9 

44 
42 

OO  - 

378 

200 

6705  ft. 

10 

40 

400 

A  TT£iT»o  em 

rl  i  o+  a  i-n->*i  Q 

Q  r;  f  <- 

36 


1552 


14 

20 
26 
19 
24 


38 
36 
34 
32 
30 


532 

720 
884 
608 
720 


103 


3464 


16 

10 

10 

6 

6 


28 
26 
24 
22 
20. 


448 
260 
240 
132 
120 


1200 


26 


TABLE  5. 
Results  obtained  by  making  tests  with  the  20  ft.  letters : 


(A) 
4 
7 
6 


17 

19 
21 
31 
35 
38 

144 


(B) 
34 
32 
30 


28 
26 
24 
22 
20 


(C) 
136 

224 
180 

540 

532 
546 

744 
770 
760 

3352 


12 

18 

216 

11 

16 

176 

7 

14 

98 

3 

12 

36 

2 

10 

20 

1 

8 

8 

3 

6 

18 

39 


200 


572 


4438  ft. 


Average  distance:  22.2  ft. 


TABLE  6. 
Results  obtained  by  making  tests  with  the  20  ft.  dots : 


(A) 

i 

2 
5 

8 


135 


(B) 
34 
32 
30 


(C) 
34 

64 
150 

248 


12 

28 

336 

11 

26 

286 

30 

24 

720 

45 

22 

990 

37 

20 

740 

3072 


25 

18 

450 

12 

16 

192 

8 

14 

112 

3 

12 

36 

4 

10 

40 

1 

8 

8 

3 

6 

18 

0 

4 

0 

1 

2 

2 

57  858 

200  4178ft. 

Average  distance:  20.9ft. 


27 

TABLE  7. 
Results  obtained  by  making  tests  with  the  16  ft.  letters 

(A)         (B)  (C) 

2          28  56 

1          26  26 

4  24  96 

18  22  396 

29  20  580 


54  1154 


59 

18 

1062 

34 

16 

544 

30 

14 

420 

9 

12 

108 

6 

10 

60 

4 

8 

32 

2 

6 

12 

1 

4 

4 

1 

3 

3 

146  2245 


200  3399ft. 

Average   distance:    16.9  ft. 


TABLE  8. 
Results  obtained  by  making  tests  with  the  12  ft.  letters 


(A)  (B)  (C) 

12  18  216 

36  16  576 

47  14  658 

50  12  600 


145  2050 


23 

10 

230 

21 

8 

168 

5 

6 

30 

3 

4 

12 

2 

2 

4 

1 

1 

1 

55  445 


200  2495  ft. 

Average   distance:    12.5  ft. 


28 

The  combined  distance  at  which  the  12  ft.  letters  could 
be  seen  was  2,495  ft.  This  divided  by  200,  equals  12.48  ft., 
the  average  distance  at  which  the  12  ft.  letters  were  seen. 

Putting  these  results  in  tabular  form  we  have : 

TABLE  9 
Average  distance  at  which 

50  ft.  letters  could  be  seen  54.47  ft. 

40  ft.  "  "  43.13  ft. 

30  ft.  "  "  "  "  33.5  ft. 

20  ft.  "  "  "  "  22.2  ft. 

20  ft.  dots  "  "  "  20.9  ft. 

16  ft.  letters  "  "  "  16.94  ft.  . 

12  ft.  "  "  12.48  ft. 

If  each  one  of  these  different  sized  letters  and  the  dot 
has  the  same  value  in  making  tests,  then  the  fraction  ex- 
pressing the  acuteness  of  vision  as  shown  by  the  50  ft.  let- 
ter test  will  be  equal  in  value  to  the  fraction  representing 
the  acuteness  of  vision  as  shown  by  the  tests  made  by  the 
40  ft.  letter,  the  30  ft.  letter,  and  so  on,  to  the  fraction 
representing  the  acuteness  of  vision  as  shown  by  the  12  ft. 
letter  test.  In  other  words,  the  fractions  representing  the 
acuteness  of  vision  as  shown  by  making  tests  with  each  of 
the  different  sized  letters  and  the  dots  will  be  equal  in 
value. 

How  nearly  this  proved  to  be  true  with  the  tests  under 
consideration  is  shown  in  Table  10.  The  first  fraction  was 
obtained  by  adding  the  numerators  of  each  of  the  200  frac- 
tions representing  the  acuteness  of  vision,  as  shown  by  each 
test  with  the  50  ft.  letter,  and  placing  this  sum  over  the 
sum  of  all  the  denominators,  which  of  course,  was,  in  this 
case,  200x50,  because  there  was  a  fraction  for  each  of  the 
200  pupils  tested  and  the  denominator  representing  the 
acuteness  of  vision  was  always  50. 

The  second  and. all  the  other  fractions  were  obtained 
in  exactly  the  same  way,  except  that  the  denominators  of  the 
respective  fractions  were  obtained  by  multiplying  200  by 
40,  30,  20,  etc. 


29 

TABLE  10 

Fractions  showing  the  acuteness  of  vision  of  200  pupils 
when  tested  by  the 

10894 

50  ft.  letters  or  expressed  decimally     1.089 

10000 

8625 
40  ft.       "  "          "  "  1.077 

8000 

6705 

30  ft.       »  "          »  "  1.118 

6000 

4474 

20  ft.       "  "          "  "  1.119 

4000 

4186 

20  ft.  dots  "          "  "  1.046 

4000 

3387 

16  ft.  letters        "    "       "     1.056 
3200 

2495 

12  ft.   "          "    "        "     1.04 
2400 

Of  course,  if  each  of  the  200  pupils  had  tested  up  to 
normal  with  each  kind  of  test  the  fractions  would  not  only 
have  been  equal  in  value  but  each  would  have  been  equal  to 
one  or  unity.  The  decimal  parts  of  the  numbers  in  the 
column  to  the  right  show  just  how  much  each  test  is  away 
from  the  normal.  Thus  the  first  decimal  .089  means  that 
tests  made  with  the  50  ft.  letters  averaged  .089  of  50  ft. 
above  normal  or  4.45  ft.  The  next  decimal  .077  means  that 
tests  made  with  the  40  ft.  letter  yield  results  .077  of  40  ft. 
or  3  ft.  above  normal,  etc. 


30 

If  we  take  the  decimal  .077  which  shows  the  variation  of 
the  results  obtained  by  the  40  ft.  letter  test,  as  the  mean 
variation,  then  the  variation  of  each  of  the  other  decimals 
from  this  mean  would  give  a  result  so  small  that  it  could 
be  neglected  in  any  ordinary  tests  for  acuteness  of  vision 
with  any  of  the  letters  or  dots. 

These  fractions  not  only  show  that  the  amount  of  vari- 
ation of  each  kind  of  test  from  the  mean  variation  is  slight, 
but  that  all  of  these  variations  are  uniformly  above  normal. 

The  fact  that  each  one  of  these  tests  shows  but  little 
variation  from  the  normal  or  from  the  mean  variation  does 
not,  within  itself,  necessarily  mean  that  each  is  equally  val- 
uable for  making  tests  of  acuteness  of  vision.  Grave  errors 
may  exist  of  a  plus  and  a  minus  nature,  but  of  magnitude 
so  nearly  equal  as  not  to  be  disclosed  by  mere  averages. 

The  exact  location  and  the  exact  extent  of  these  varia- 
tions from  the  assumed  normal  is  shown  in  tables  2  to  8. 
A  glance  at  these  tables  shows  at  once  the  number  of  pupils 
(column  A),  who  could  see  the  different  tests  at  different 
distances.  These  same  facts  are  graphically  represented 
in  graphs  4,  5,  and  6.  These  graphs  not  only  represent  the 
number  and  extent  of  the  variation  from  the  normal,  but 
graph  4  shows  the  variation  of  these  in  the  12  ft.,  16  ft.,  and 
20  ft.  letter  tests  both  from  the  normal  and  from  each  other. 
Graph  5  shows  the  same  facts  in  reference  to  the  20  ft.  let- 
ter test  and  the  20  ft.  dot  test.  Graph  6  showrs  these  facts 
in  reference  to  tests  made  with  the  30  ft.,  40  ft.,  and  50  ft. 
letter  tests. 

In  each  one  of  the  graphs  the  line  a-b  represents 
the  assumed  distance  at  which  the  normal  eye  could  just 
make  out  the  letters  or  dots. 

The  vertical  column  of  numbers  at  the  left  represents 
the  number  of  pupils  who  could  see  the  tests  at  the  differ- 
ent distances. 

The  horizontal  line  of  figures  beneath  the  curves  in- 
creases by  two's,  both  right  and  left,  beginning  at  the  base 
of  the  line  a-b,  and  shows  the  number  of  feet  variation  from 
the  normal,  a-b,  made  by  each  group  of  pupils,  indicated  by 
the  vertical  line  of  figures  at  the  left.  The  figures  to  the 
left  of  the  base  of  line  a-b  represent  the  distance  above 
normal  and  the  figures  to  the  right,  the  distance  below  nor- 
mal. 


31 


PupilS 
40 
art 

ft       . 


so 
fi 


36 

4 
3H 
3Q 
Jfl 
16 

M 
& 

H> 

K 
/6 
M 
A 
» 
f 
6 
4- 


Dumber  of  feet  variation  on  either  side  of  normal. 
Right  side  is  above  normal,  left  side  below  normal. 


GKAPH  4. 


32 


Pupils 


f* 
4* 
V> 

St. 

<* 
31 
A 

23 
26 
A* 


It 
* 
* 
A 

* 
9 
6 


/r 


Number  of  feet  variation  on  either  side  of  normal 
$ide  is   above  normal,    left 


GEAPH  5. 


33 


£3 


34 

If  all  of  these  seven  tests  had  been  of  equal  value  in 
testing  normal  vision  and  those  above  and  below  normal, 
and,  if  the  curves  representing  these  results  had  all  been 
placed  in  one  figure,  then  the  apexes  of  each  of  these  curves 
would  either  have  been  on  the  line  a-b  or  some  other  line 
parallel  to  line  a-b. 

Furthermore,  the  curve  representing  the  results  obtain- 
ed by  testing  with  the  50  ft.  letters  would  have  its  apex 
higher  than  any  other  curve  and  the  distance  between  the 
two  ends  of  the  curves  would  be  greater  than  the  distance 
between  the  ends  of  any  of  the  other  curves.  Immediately 
under  this  curve  with  its  apex  on  the  same  vertical  line 
with  the  apex  of  the  50  ft.  curve  and  with  its  two  ends  less 
distance  apart  would  come  the  40  ft.  curve.  Then  would 
follow  the  30  ft.,  20  ft.,  16  ft.  and  12  ft.  curves  in  order,  each 
being  not  so  high  or  wide  as  its  predecessor  and  the  sides  of 
each  would  be  parallel  with  the  50  ft.  curve,  and,  of  course, 
with  each  other,  also. 

The  curve  for  the  20  ft.  letters  and  the  curve  for  the  20 
ft.  dots,  theoretically,  should  be  the  same,  and,  of  course, 
would  be  represented  by  one  and  the  same  curve,  if  placed 
in  the  same  graph. 

It  was  found  impractical  to  put  all  of  these  curves  in 
one  graph,  so  they  are  shown  in  three  graphs :  4,  5  and  6. 

A  glance  at  these  graphs  shows  at  once  that  no  two 
curves  are  parallel  and,  consequently,  the  results  of  no  two 
tests  are  uniform.  As  a  matter  of  fact,  no  two  such  curves 
will  ever  be  parallel,  even  if  the  tests  used  were  of  equal 
value  as  tests,  for  the  personal  element,  of  both  the  oper- 
ator and  the  subject,  and  the  influence  of  environment  are 
constantly  injecting  themselves  into  and  modifying  the  re- 
sults, consequently,  variations  of  these  curves  from  each 
other  are  to  be  expected  within  certain  limits.  We  can  pre- 
scribe these  limits,  however,  and  require  that  results  from 
tests  obtained  by  using  any  size  letter  and  character  shall 
come  within  these  limits. 

It  would  be  fair,  it  seems,  in  making  tests  with  different 
sized  letters  and  characters  to  expect  that  the  numbers  who 
could  see  these  letters  and  characters  further  than  12%% 
of  the  selected  normal  distance  should  be  fairly  constant. 

The  same  requirement  might  be  made  for  the  lower  limit 
of  vision  with  these  same  tests.  That  is,  the  number  un- 


35 

able  to  see  each  test  without  moving  nearer  to  the  test  than 
12%%  of  the  selected  normal  distance  should  be  fairly  con- 
stant. 

If  this  limit  were  not  broad  enough  then  any  percentage 
of  the  normal  distance  above  or  below  the  normal  greater 
than  12i/2%  might  be  taken,  as  25%,  37%,  or  50  %,  and  we 
could  require  that  the  number  seeing  the  different  tests 
further  than  normal  by  these  percentages  should  be  fairly 
constant,  and,  that  the  number  who  could  not  see  the  same 
tests  without  getting  nearer  to  them  than  the  percentages 
of  the  normal  distance  indicated,  should  also,  be  fairly 
constant.  Both  of  these  methods  of  determining  whether  a 
test  is  reliable  or  not  has  value.  If  it  is  desirable  to  deter- 
mine how  acute  the  vision  of  a. pupil  is  who  has  acute  vision, 
then  the  upper  limit  method  of  trying  out  the  tests  will  be 
of  value.  If,  however,  it  is  desired  to  know  how  acute  the 
vision  of  a  pupil  is  who  cannot  see  the  test  as  far  away  as 
the  normal  distance,  then  the  lower  limit  method  will  be  of 
value.  But,  since  most  pupils  are  supposed  to  have  some- 
where near  normal  vision,  it  would  seem,  if  the  correct 
tests  are  used,  that  the  number  seeing  these  tests  at  normal 
and  a  certain  percentage  above  and  below  the  normal  dis- 
tance should  be  fairly  constant,  for  all  the  tests.  This 
might  be  called  the  mean  limit  of  tests  for  acuteness  of 
vision.  These  methods  of  determining  the  relative  value 
of  testts  have  been  used  in  connection  with  the  seven  dif- 
ferent tests  under  consideration  and  the  results  are  shown 
in  table  11. 

The  (a)  portion  of  this  table  represents  the  results  ob- 
tained by  applying  what  has  been  called  the  "upper  limit 
test,"  for  the  given  percentages  above  normal,  to  the  re- 
sults obtained  from  each  of  the  seven  tests. 

In  (b)  is  shown  the  result  of  applying  the  "lower  limit 
test, ' '  with  the  same  percentages,  to  the  results  of  the  same 
tests. 

In  (c),  is  shown  the  results  of  applying  the  "mean  limit 
test,"  with  the  same  percentages,  to  the  results  of  the  same 
tests.  The  uniformity  of  the  results  shown  in  (b)  by  apply- 
ing the  "lower  limit  test"  is  quite  striking  in  the  12%% 
line  except  the  numbers  under  the  16  ft.  and  the  12  ft.  let- 
ters and  a  close  degree  of  uniformity  in  all  the  tests,  is 
also  seen  in  the  25%,  37%%,  and  50%  lines,  respectively. 


36 


w 


cn 
O 

CO 

-q 

to 

cn 

O 

cn 

0 

CO 

to 

cn 

o 

cn 

s 

CO 

to 

cn 

o 

^ 

W    Ul 

^g 

i_i 

i9 

HI   W 

o* 

o]  ® 

O^ 

to  ^ 

• 

<o^ 

to  (t> 

0>    2. 

J^  » 

vj^  ® 

0  uq 

s^  5 

^WJ 

P 

Mi 

3    (-+ 

e 

0 

o 

•-j 

M 

8 

T> 

M   P 

p 

3 

to  3 

xH    Oj 

3 

3 

10 

O 

O 

^  o 

* 

.     3 

3 

'. 

•      0* 

•    "J 

h-  ' 
00 

-q 

CO 

CO 

to 

to 

CO 

S"s 

CO 

j—  i 

0 

o 

o 

1—  1 

00 

cn 

0 

a? 

oo 

-q 

1—  ' 

co 

CO 

CO 

-q 

ra 

co 

00 

05 

00 

00 

to 

-q 

CO 

00 

0 

3P 

^    \ 

i—  i 

00 

.<j 

4^- 

oo 

H-L 

CO 

to 

CO 

oo 

f^-        ^ 

00 

to 

cn 

cn 

cn 

00 

to 

-q 

o 

CO 

3  P 

oo 

1—  ' 
-q 

CO 

1—  I 

CO 

-q 

f8 

cn  . 

00 

S 

iffc 

CO 

05 

to 

O5 

to 

3  F 

oo 

oo 

M 

M 

to 

CO 

CO 

05 

Og 

oo 

0 

CO   . 

-q 

cn 

to 

o 

to 

.CO 

oo 

1—  I 

' 

CO 

M 
00 

I—  I 

O 

M 

to 

to 

cn 

fs 

CO 

cn 

1—  1 

05 

oo 

CO 

CO 

-q 

cn 

IF 

CO 

00 

M 

00 

to 

i—1 

-q 

r_ 

05 

-q 

cn 

05 

oo 

0 

to 

00 

3  F 

P: 


^ 
tf 

^ 


II 


CD  ^ 

%S  O 

s  & 

-d  H— 

•*H  O 

CT> 


O3     CD 

i? 

03 1— i 

^  S- 

c-K 

S^    ^ 
O      O2 


& 


37 

According  to  these  figures,  either  one  of  the  tests  ex- 
cept the  12  ft.  letter  test  could  be  relied  upon  to  detect 
vision,  that  is  less  than  50%  of  normal,  or  37%  %  or  25% 
or  even  12%%  of  normal.  Since  the  detection  of  poor 
vision,  rather  than  the  determination  of  how  many  have 
acute  vision,  above  normal,  is  the  chief  purpose  of  testing 
the  vision  of  school  children,  any  of  the  seven  tests  under 
consideration  except  the  12  ft.  letter  test  would  be  adequate 
for  this  purpose,  especially  is  this  true,  if,  as  is  usually  the 
case,  only  those  pupils  who  have  vision  less  than  25%  nor- 
mal are  given  attention. 

By  inspection  of  the  (c)  portion  of  table  11  or  that  por- 
tion showing  the  mean  variation  from  the  normal,  we  see 
here,  too,  a  rather  close  degree  of  uniformity  of  results. 
This  is  especially  marked  in  the  figures  showing  variations 
on  both  sides  of  the  normal  of  more  than  25%,  and,  it 
would  seem  reasonable  to  expect  that  any  vision  test  that 
makes  any  pretension  to  reliability  should  show  similar  re- 
sults when  this  test  is  applied. 

If  we  now  give  our  attention  to  the  (a)  portion  of  table 
11,  we  see  here,  too,  a  rather  close  degree  of  uniformity  in 
all  the  tests  for  the  upper  limit  of  vision  for  all  the  per- 
centages taken  above  normal.  Since  the  application  of  all 
of  these  tests  to  the  tests  under  consideration  give  fairly 
uniform  results,  it  is  reasonable,  it  seems,  to  conclude  that 
the  results  in  general  will  be  about  as  accurate  with  one 
test  as  with  another.  Exceptions,  however,  will  have  to  be 
made  with  the  12  ft.  letter  tests,  although  the  figures  in  the 
tables  would  seem  to  indicate  that  this  test  is  generally 
about  as  good  as  any  of  the  other  tests.  This  exception 
will  have  to  be  made  in  spite  of  these  figures,  because  in  at 
least  two  cases  of  undoubted  nearsightedness,  the  pupils 
could  not  see  the  larger  letters  at  anything  like  the  normal 
distance,  but  they  could  see  the  12  ft.  letters  at  about  nor- 
mal. 

The  variation  of  results  of  certain  tests  from  the  results 
of  other  tests  as  shown  in  table  11  demands  some  attention. 

In  the  (a)  portion  of  the  table  it  is  noted  that  the  num- 
ber seeing  the  20  ft.  dots  beyond  the  normal  distance  by  the 
different  given  percentages  is  smaller  in  every  case  than 
with  any  of  the  other  tests  except  the  16  ft.  letter.  From 
the  data  obtained  from  these  tests  it  is  not  possible  to  as- 


38 

sign  a  reason  why  the  16  ft.  letters  were  not  seen  as  far 
proportionately  above  the  normal  as  were  the  twenty  ft. 
letters  or  any  of  the  other  letters,  but  it  is  believed  that  the 
failure  to  see  the  20  ft.  dots  as  far  as  the  letters,  can  be 
accounted  for  in  this  way.  In  deciding  what  a  letter  is, 
the  element  of  intelligence  as  well  as  the  ability  to  see 
enters  in  as  a  determining  factor  much  oftener  than  is  the 
case  with  deciding  whether  the  dot  is  seen  or  not. 

In  seeing  the  dot  only  two  things  can  enter  into  the  mind 
on  which  a  decision  is  to  be  made,  and  these  two  things  are, 
is  the  dot  there,  or  is  it  not  there,  or  does  the  dot  make  a 
sensation  on  the  retina  or  does  it  not.  The  decision  that  is 
made  will  depend  almost  exclusively  upon  pure  retinal  sen- 
sation. While  in  the  case  of  seeing  the  letter  there  can  be 
no  doubt  that  the  letter  is  seen,  that  a  retinal  impression  is 
made,  but  in  deciding  what  the  letter  is  that  is  making  this 
particular  impression,  often,  undoubtedly,  involves  a  com- 
plicated mental  operation,  in  which  the  general  shape  and 
appearance  of  the  letter  play  a  very  important  part. 
Hence,  one  must  expect  fewer  pupils  to  see  the  20  ft.  dot 
at  distances  considerably  above  normal  than  will  see  the 
same  sized  letters  or  letters  of  any  size  at  proportional  dis- 
tances. 

This  expectation  is  borne  out  by  the  figures  in  (b),  table 
11.  Here  it  is  seen  that  the  dot  shows  up  more  pupils  with 
defective  vision,  on  the  average  than  any  of  the  letter  tests, 
at  the  percentages  below  normal  given,  except  the  12  ft. 
letter. 

The  figures  in  (c)  under  the  20  ft.  dot  column  also  show 
that  the  letters  of  all  sizes  above  the  16  ft.  letters  can  be 
seen  better  than  the  20  ft.  dot  at  the  same  relative  distances. 
Take,  for  example,  the  12%%  variation  on  either  side  of 
normal,  there  were  only  90  pupils  who  could  not  read  the  50 
ft.  letters,  while  there  were  117  who  could  not  make  out 
the  dot  at  the  same  relative  distance  from  normal.  The 
fact  that  the  vision  of  the  200  pupils  tested  averaged 
above  normal  and  that  more  pupils  saw  the  20  ft.  dots  at 
the  average  distance  above  normal  than  for  any  of  the  other 
tests,  and,  since  the  number  found  with  defective  vision 
was  unusually  small,  but  the  dot  test  showed  more  than 
any,  one  would  be  inclined  to  the  belief  that  the  dot  is  the 
best  of  any  of  the  tests  used.  One  would  be  justified  in 


39      V/    :  .::"-  ^ '' ^ 

coming  to  this  conclusion,  not  only  because  it  tests  vision, 
and  vision  only,  and  the  results  are  more  in  harmony  with 
what  other  investigators  have  found  out  about  the  number 
of  children  who  have  defective  vision,  but,  also,  because  of 
the  simplicity  of  the  test  and  the  fact  that  it  can  be  used  to 
test  little  children,  illiterates  or  literates  with  equal  ease 
and  accuracy.  Further  evidence  that  the  dot  is  a  good  test 
is  shown  by  the  fact  that  there  was  not  a  single  case  of  poor 
vision  detected  among  the  200  pupils  by  any  of  the  other 
tests  that  was  not  also  detected  by  the  dot  test.  This  was 
also  true  with  the  tests  made  with  the  16  ft.  and  the  12  ft. 
letter,  except  in  the  two  cases  mentioned  above.  This 
shows  undoubtedly  that  for  certain  defects  of  the  eye  the 
12  ft.  letters  are  not  reliable.  The  16  ft.  letters  were  found 
to  be  reliable  for  the  detection  of  all  cases  of  poor  vision 
that  would  need  attention  and  which  were  detected  by  the 
other  tests. 

The  results  of  these  tests  clearly  justify  one  in  drawing 
the  following  conclusions : 

1.  The  "illiterate  E"  as  now  constructed  is  practically 
useless  as  a  test  of  the  acuteness  of  vision.    If  it  is  to  be 
used  as  a  test  when  constructed  of  the  size  of  the  16  ft.  let- 
ter, then  the  distance  at  which  it  should  be  placed  from  the 
one  being  tested  should  be,  not  16  ft.,  but  26  ft.    Or,  if  the 
16  ft.  distance  is  to  be  maintained  then  the  size  of  the  letter 
must  be  reduced  to  16/26  of  its  present  size. 

2.  The  20  ft.  dot  test  is  thoroughly  reliable  for  testing 
poor  vision,  normal  vision,  or  acute  vision.    None  of  the  200 
pupils  tested  seemed  to  have  any  optical  trouble — myopia, 
hyperopia,  astigmatism  or  any  other  optical  defect — that 
was  not  detected  by  this  test  as  well  or  better  than  by  any 
other  test. 

3.  The  16  ft.  letter  test  is  reliable  for  all  defects  of  suffi- 
cient gravity  to  justify  the  teacher  in  recommending  the 
pupil  to  go  to  an  oculist. 

4.  The  12  ft.  letter  test  will  detect  most  of  the  graver 
defects  of  vision,  but  not  all,  therefore,  it  is  not  to  be  relied 
upon. 

5.  The  eyes  of  150  of  the  200  pupils,  subjected  to  these 
tests  were  tested,  one  eye  at  a  time,  a  few  weeks  before. 


40 

Every  pupil,  with  four  exceptions,  who  had  vision  25%  or 
more  below  normal,  as  shown  by  this  one-eye-at-a-time  test, 
could  with  two  eyes  make  a  better  showing.  Not  only  was 
this  true  of  pupils  having  poor  vision,  but  it  was  equally 
true  of  all  other  pupils.  This  can  be  taken  as  an  indication, 
not  only,  that  binocular  vision  is  better  than  monocular 
vision,  but  it  accounts  for  the  fact  that  the  pupils  in  these 
tests  averaged  above  normal  in  vision. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 

AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $t.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


F£8    7 


1935 


19 


THE    MODERN    PR|NT    SHOP 
TRENTON.   N.   J. 


5V 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


